Prep the rice and mise en place: have 1 cup cooked brown rice hot or warm and ready. Thinly slice the steak across the grain into 1/8–1/4-inch slices; this shortens the muscle fibers and makes the beef tender when chewed. Pat the slices dry with paper towels—moisture prevents a good sear.

Make a quick marinade to add flavor and protect the meat: in a bowl combine 1 tablespoon of the soy sauce with the cornstarch and 1 teaspoon cold water to make a thin slurry. Toss the beef slices with this mixture and a pinch of black pepper and let sit 8–12 minutes. The cornstarch gives the meat a slight velvety coating ('velveting') that improves texture and helps the sauce cling.

Prepare the vegetables and aromatics: trim broccoli into small florets, seed and slice the bell pepper, and cut carrots into matchsticks or 1/8" slices so everything cooks quickly and evenly. Mince the garlic and grate the ginger together—these aromatics will be added near the end to preserve brightness and fragrance.

Mix the finishing sauce: in a small bowl combine the remaining 1 tablespoon soy sauce, the remaining 1 tablespoon oil (sesame or olive), and 1 tablespoon cold water. Taste and adjust: if you prefer a slightly sweeter glaze add 1 teaspoon honey or brown sugar (optional). Keep the sauce nearby—stir-frying moves fast.

Heat the pan properly: place a wok or heavy skillet over high heat until very hot (a few drops of water should sizzle away instantly). Properly preheating creates the Maillard reaction (browning) that builds savory flavor. If your oil has a low smoke point (extra-virgin olive oil), add a teaspoon of neutral oil first.

Sear the beef in batches: add 1 tablespoon sesame oil to the hot pan, swirl to coat. Add half the beef in a single layer and let it sit 20–30 seconds to develop a caramelized edge before stirring—constant crowding cools the pan and causes steaming instead of searing. Sear each batch quickly (about 60–90 seconds) until just browned but still medium-rare to medium—the beef will finish cooking with the sauce. Remove seared beef to a plate and reserve.

Cook the vegetables to crisp-tender texture: if needed add a splash more oil, then add the carrots first (they take longest), stir 30–45 seconds, then add broccoli and bell pepper. Keep the vegetables moving in the pan so they cook quickly and keep bright color and snap—overcooking makes them limp and dull. Cook until they are bright and just tender, about 2–3 minutes total depending on heat and pan.

Add aromatics and deglaze: push the vegetables up the sides of the wok, add the grated ginger and minced garlic to the center and stir for 10–15 seconds until fragrant. Pour the prepared sauce into the pan to deglaze—this loosens the browned bits (fond) that contain concentrated flavor.

Thicken and finish: whisk 1 teaspoon cornstarch with 1 tablespoon cold water to make a smooth slurry (if you already used the cornstarch for the marinade, use another small pinch). Pour the slurry into the wok, stirring constantly; the sauce will thicken in 20–30 seconds into a glossy glaze that clings to the beef and vegetables—this texture is what elevates the dish from a simple stir-and-serve to restaurant quality.

Return the beef and toss: add the seared beef back into the wok and toss everything for 30–45 seconds to combine and warm through. Taste and adjust for salt/sweetness (add a pinch of salt or a dash more soy if needed). Finish with a small drizzle (optional) of sesame oil for aroma—do this last because sesame oil loses its fragrance if cooked too long.

Plate and garnish: spoon the warm brown rice onto two plates, mound the beef and vegetables on top, and scatter sliced scallions and toasted sesame seeds if using. Serve immediately while the contrast between hot stir-fry and nutty rice is at its best.